who can show me step by step on how to differentiate f(x)= (-x^2-1)/(x^2-1)^2. please do so. The answer must be f'(x)=(2x^3+6x)/(x^2-1)^3 or it is a wrong answer

Have you given it any thought?

Take the first function as (-x^2-1) and the second as (x^2-1)^2, and use the quotient rule for differentiation:

d(u/v)/dx = (u'v - v'u)/v^2